Which equation represents the graphed function? \u20133x 2 = y \u2013x 2 = y x \u2013 3 = y 2x \u2013 3 = y<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine which equation represents the graphed function, we first need to understand the general form of each equation and how it relates to the graph. Each equation describes a linear or quadratic relationship between (x) and (y). Let\u2019s analyze each option one by one:<\/p>\n\n\n\n This equation is quadratic, meaning it represents a parabolic graph. The negative coefficient ((-3)) in front of (x^2) indicates that the parabola opens downward, and the graph will be symmetric along the y-axis. The vertex of the parabola will be at the origin ((0, 0)) because there are no linear or constant terms. This type of graph typically has a “frown” shape, where the arms of the parabola open downward.<\/p>\n\n\n\n Similar to the first equation, this is also a quadratic equation, but with a coefficient of (-1) instead of (-3). This means the graph will still be a downward-opening parabola, but the “width” of the parabola will be different. Specifically, the graph will be wider than the one represented by (-3x^2 = y), because the coefficient is smaller in magnitude. It will also have its vertex at the origin ((0, 0)).<\/p>\n\n\n\n This is a linear equation in slope-intercept form. Rearranging it gives (y = x – 3). The equation represents a straight line with a slope of 1 and a y-intercept of (-3). This means the line will cross the y-axis at ((0, -3)) and will rise 1 unit for every 1 unit it moves to the right.<\/p>\n\n\n\n This is another linear equation in slope-intercept form. Rearranging it gives (y = 2x – 3). This equation represents a straight line with a slope of 2 and a y-intercept of (-3). The line will be steeper than the previous one (slope = 1) and will also cross the y-axis at ((0, -3)).<\/p>\n\n\n\n To determine which equation best represents the graph, we need to consider the shape of the graph. If the graph is parabolic (either opening upward or downward), options 1 and 2 are likely the correct choices. However, if the graph is a straight line, options 3 and 4 are more appropriate. Based on the description provided, the correct answer depends on the specific graph<\/strong>. If the graph is parabolic, then (-3x^2 = y) (option 1) or (-x^2 = y) (option 2) are correct, and if the graph is linear, then (x – 3 = y) (option 3) or (2x – 3 = y) (option 4) are correct.<\/p>\n\n\n\n Given the information provided, option 3<\/strong> or option 4<\/strong> would represent a linear graph, while option 1<\/strong> or option 2<\/strong> would represent a parabolic graph.<\/p>\n","protected":false},"excerpt":{"rendered":" Which equation represents the graphed function? \u20133x 2 = y \u2013x 2 = y x \u2013 3 = y 2x \u2013 3 = y The Correct Answer and Explanation is: To determine which equation represents the graphed function, we first need to understand the general form of each equation and how it relates to the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-168975","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=168975"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168975\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Option 1: (-3x^2 = y)<\/h3>\n\n\n\n
Option 2: (-x^2 = y)<\/h3>\n\n\n\n
Option 3: (x – 3 = y)<\/h3>\n\n\n\n
Option 4: (2x – 3 = y)<\/h3>\n\n\n\n
Conclusion<\/h3>\n\n\n\n